Algebra & Number Theory
- Algebra Number Theory
- Volume 8, Number 10 (2014), 2433-2469.
A $p$-adic Eisenstein measure for vector-weight automorphic forms
We construct a -adic Eisenstein measure with values in the space of vector-weight -adic automorphic forms on certain unitary groups. This measure allows us to -adically interpolate special values of certain vector-weight automorphic forms, including Eisenstein series, as their weights vary. This completes a key step toward the construction of certain -adic -functions.
We also explain how to extend our methods to the case of Siegel modular forms and how to recover Nicholas Katz’s -adic families of Eisenstein series for Hilbert modular forms.
Algebra Number Theory, Volume 8, Number 10 (2014), 2433-2469.
Received: 3 March 2014
Revised: 22 September 2014
Accepted: 3 November 2014
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 11F03: Modular and automorphic functions
Secondary: 11F33: Congruences for modular and $p$-adic modular forms [See also 14G20, 22E50] 11F30: Fourier coefficients of automorphic forms 11F55: Other groups and their modular and automorphic forms (several variables) 11F85: $p$-adic theory, local fields [See also 14G20, 22E50] 11F46: Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms
Eischen, Ellen. A $p$-adic Eisenstein measure for vector-weight automorphic forms. Algebra Number Theory 8 (2014), no. 10, 2433--2469. doi:10.2140/ant.2014.8.2433. https://projecteuclid.org/euclid.ant/1513730330